Compound Shapes interactive worksheet - Free Printable

I'll solve each compound shape perimeter problem step by step.

Problem 1:
- Given sides: 14 cm, 14 cm, 5 cm
- The shape is a rectangle with a triangle attached
- Left side = 14 cm, bottom = 14 cm, top slanted side = 5 cm
- Right side has two parts that equal the left side (14 cm)
- Top horizontal part equals bottom (14 cm) minus the horizontal projection of the slanted side
- Actually, looking at this more carefully: it's a pentagon
- Sides are: 14 + 14 + 5 + (need to find remaining sides)
- The right side consists of a vertical and diagonal part
- If we trace around: 14 (left) + 14 (bottom) + 5 (diagonal) + ? + ?
- The top must connect back, so there's a horizontal top segment
- Since it looks like a rectangle with a triangular extension on the right:
- Perimeter = 14 + 14 + 5 + 5 + 14 = 52 cm (if symmetric)

Let me reconsider: This appears to be a rectangle (14×14) with an isosceles triangle attached to the right side where the base of the triangle replaces part of the rectangle's right side.
- If the slanted side is 5 cm and it's symmetric, both slanted sides = 5 cm each
- But only one 5 cm is labeled
- Looking again: it seems like a pentagon with sides 14, 14, 5, and two unknown sides on the right
- Actually, the simplest interpretation: add all visible outer edges
- Going clockwise from top-left: horizontal top edge + 5 cm diagonal + vertical right edge + 14 cm bottom + 14 cm left
- If it's a regular shape, the missing sides would make it complete
- Most likely answer: 14 + 14 + 5 + 5 + 14 = 52 cm

Problem 2:
L-shaped figure:
- Top horizontal: 11 cm
- Right vertical (top): 11 cm
- Inner horizontal: 10 cm
- Right vertical (bottom): 10 cm
- Bottom horizontal: 20 cm
- Left vertical: 21 cm

Perimeter = 11 + 11 + 10 + 10 + 20 + 21 = 83 cm

Problem 3:
L-shaped figure:
- Top: 18 cm
- Right vertical (top section): need to calculate
- Inner horizontal: 16 cm
- Right vertical (bottom): 16 cm
- Bottom: need to calculate
- Left: 19 cm

The inner corner creates:
- Vertical drop from top right = 19 - 16 = 3 cm
- Horizontal extension on bottom = 18 + 16 = 34 cm... wait, that doesn't look right

Let me reconsider: Going around the outside:
- Top: 18 cm
- Right side going down: (19 - 16) = 3 cm, then over 16 cm, then down 16 cm
- Bottom: 18 + 16 = 34 cm? No...

Actually for L-shapes, perimeter = sum of all outer edges:
- Left: 19 cm
- Top: 18 cm
- Right upper vertical: (19 - 16) = 3 cm
- Inner horizontal: 16 cm
- Right lower vertical: 16 cm
- Bottom: 18 + 16 = 34 cm

Total = 19 + 18 + 3 + 16 + 16 + 34 = 106 cm

Hmm, let me think differently. For L-shapes, you can "unfold" them:
Perimeter = 2(length + width) where length and width are the overall dimensions
Overall width = 18 + 16 = 34 cm
Overall height = 19 cm
But that gives 2(34 + 19) = 106 cm... same answer

Wait, I need to be more careful. Let me trace the perimeter:
Starting from top-left, going clockwise:
1. Top edge: 18 cm
2. Down the right side of top rectangle: (19 - 16) = 3 cm
3. Across the inner corner: 16 cm
4. Down the right side of bottom rectangle: 16 cm
5. Bottom edge: 18 + 16 = 34 cm
6. Up the left side: 19 cm

Total = 18 + 3 + 16 + 16 + 34 + 19 = 106 cm

Problem 4:
Complex L-shape with measurements:
- Top: 12 m
- Right vertical (upper): 12 m
- Inner horizontal: 10 m
- Right vertical (middle): 6 m
- Bottom: 24 m
- Left vertical (lower): 2 m
- Need to find left vertical (upper)

Left upper vertical = 12 + 6 - 2 = 16 m

Perimeter = 12 + 12 + 10 + 6 + 24 + 2 + 16 = 82 m

Problem 5:
Trapezoid-like shape:
- Left vertical: 4 m
- Bottom: 4 m
- Right vertical: 2 m
- Top slanted: 16 m
- Need to find the horizontal top segment

The horizontal difference between left and right = 4 - 2 = 2 m (in height)
Using Pythagorean theorem for the slanted side: if it goes over some distance x and down 2 m to make 16 m...
Actually, looking at the shape, it seems like:
- The top has a horizontal part and a slanted part
- Or the entire top is slanted at 16 m

If the entire right-top is one slanted line of 16 m:
Perimeter = 4 + 4 + 2 + 16 = 26 m

But there might be a horizontal segment too. Let me assume the simplest: 4 + 4 + 2 + 16 = 26 m

Problem 6:
Trapezoid:
- Top: 9 m
- Right slanted: 14 m
- Bottom: 20 m
- Left vertical: 11 m

Perimeter = 9 + 14 + 20 + 11 = 54 m

Problem 7:
Pentagon (house shape):
- Left vertical: 12 cm
- Bottom: 14 cm
- Right vertical: 5 cm
- Two roof slopes: 16 cm each (assuming symmetry, though only one is labeled)

If only one slope is 16 cm and the other needs calculation... but typically these are symmetric.
Assuming both roof sides = 16 cm:
Perimeter = 12 + 14 + 5 + 16 + 16 = 63 cm

Problem 8:
T-shaped figure:
- Top horizontal: 36 m
- Right vertical (top): 36 m
- Right vertical (bottom section): 36 m
- Bottom: 60 m
- Left vertical (bottom): need to calculate
- Left vertical (top): need to calculate
- Inner horizontals on both sides

This is complex. Let me work it out:
- Overall width = 60 m
- Top width = 36 m
- So each side extension = (60 - 36)/2 = 12 m

Going around:
- Top: 36 m
- Right down (top part): 36 m
- Right horizontal inward: 12 m
- Right down (bottom part): 36 m
- Bottom: 60 m
- Left up (bottom part): 36 m
- Left horizontal outward: 12 m
- Left up (top part): 36 m

Total = 36 + 36 + 12 + 36 + 60 + 36 + 12 + 36 = 264 m

Problem 9:
L-shaped figure:
- Top: 10 m
- Right vertical (top): 8 m (since total height is 11 and bottom section is... wait)
- Actually: Left = 11 m, top = 10 m, right upper = ?, inner horizontal = 8 m, right lower = 8 m, bottom = ?

Right upper vertical = 11 - 8 = 3 m
Bottom = 10 + 8 = 18 m

Perimeter = 11 + 10 + 3 + 8 + 8 + 18 = 58 m

Let me double-check my calculations:

1) 52 cm
2) 83 cm
3) 106 cm
4) 82 m
5) 26 m
6) 54 m
7) 63 cm
8) 264 m
9) 58 m

Final Answer:
1) 52 cm
2) 83 cm
3) 106 cm
4) 82 m
5) 26 m
6) 54 m
7) 63 cm
8) 264 m
9) 58 m